The algebraic Bethe ansatz for rational braid-monoid lattice models

TL;DR

This paper develops an algebraic Bethe ansatz approach for a broad class of rational lattice models based on braid-monoid algebra, encompassing various Lie and superalgebras, and derives their eigenvalues and Bethe equations.

Contribution

It provides a unified quantum inverse scattering framework for multiple braid-monoid lattice models, including new Bethe ansatz solutions for these systems.

Findings

Eigenvectors and eigenvalues constructed for models based on B_n, C_n, D_n, and Osp algebras.

Bethe Ansatz equations formulated in terms of algebra root structures.

Unified approach applicable to a wide family of integrable models.

Abstract

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the superalgebra Osp(n|2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B_n, C_n, D_n, Osp(2n-1|2), Osp(2|2n-2), Osp(2n-2|2) and Osp(1|2n) models. The corresponding Bethe Ansatz equations can be formulated in terms of the root structure of the underlying algebra.